Decades of hard work to ensure this is possible. The technical instructions how to open a page and display it as intended are public. They are very detailed (hundreds of documents with thousands of pages) and cover every step. Various parts of the process are designed and documented by different organizations: IETF, W3C, WHATWG, ECMA.
Despite that, there are still some undocumented or non-standard behaviors in web browsers. This is sometimes intentional (they compete on having features that others don’t have), often by accident (it’s hard to write a browser, and people make mistakes). This means that not every page will open correctly in every browser. Page authors who care about this problem will avoid using the non-working features. Page authors who don’t care will put “you must use browser X” and block other browsers.
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